DISMT – Determination of Mixing Time through Color Changes
Lynn A Melton*, C.W. Lipp, R. W. Spradling, K.A. Paulson
Engineering Sciences, Fluid Mechanics and Mixing Group
Dow Chemical Company, B-1226
Freeport, TX 77541
ABSTRACT
The DISMT (“Dual Indicator System for Mixing Time”) mixing time/distance
diagnostic encodes semi-quantitative visualization of liquid/liquid mixing processes in
color changes. In DISMT, two liquids, one red and one blue, are mixed to produce a
yellow liquid. Through appropriate choice of the acid-base indicators used, and the initial
pH’s of the two solutions, the yellow liquid appears only in those regions where the mixing
fraction is within a designated fractional deviation (say 5%) of the infinite time mixing
fraction. Thus, the 95% mixing time/distance can be defined, for the whole volume of the
mixing system, as the time/distance for all of the liquid to become yellow.
This paper describes: (1) the principles underlying and choices involved in the
design of DISMT systems, (2) protocols for carrying out DISMT-based experiments, and
(3) examples of results obtained with DISMT.
Accepted for publication on Chemical Engineering Communications, (2001).
Keywords: colorimetry, diagnostic, fluid mechanics, imaging, instrumentation, mixing
*Corresponding Author: permanent address is Department of Chemistry, University of
Texas at Dallas, Box 830688, Richardson, TX, 75083-0688, fax: (972) 833-2925,
melton@utdallas.edu.
1
I.
Introduction
There are several classes or types of industrial mixing problems in which the
approach to the final homogeneous state is critical to the design engineer. The problems
can be as commonplace as the tank mix blend time for homogeneous blending operation or
as specific as the design of a continuous reactor in which a static or dynamic mixer is
required in order to minimize formation of undesired byproduct. Frequently, a
characteristic mixing time has been used to provide an (oversimplified) summary of the
mixing process. However, in those cases in which the development of the design permits
the use of an optically accessible mixing system, a much more informative variety of fluid
flow and mixing diagnostics may be applied. This paper describes one such diagnostic.
Mixing is fundamentally the evolution in time of spatially dependent
concentrations toward a final homogeneous state. In an ideal world, researchers studying
mixing processes would have access to concentration maps of the relevant species in the
entire vessel as a function of time. In the current world, researchers have to deal with less
than ideal data. Chemical sampling is intrusive and provides point-wise data at very low
sampling rates. Colorimetric probes are intrusive and provide point-wise data as a
continuous function of time. Planar laser induced fluorescence measurements are nonintrusive and provide 2-D concentration images, at typical sampling rates of only a few
hertz. Other useful techniques fall within these bounds. All fall considerably short of the
goal of quantitative concentrations measured non-intrusively for the whole volume of the
vessel at arbitrary sampling times. The reaction-based colorimetric diagnostic method
described in this report attempts to address part of these limitations; it provides semiquantitative, but valuable, concentration information coupled with the possibility of
complete interrogation of the vessel volume and arbitrarily fast time sampling.
DISMT (“Double Indicator System for Mixing Time”) reduces the range of
concentration information reported to the question “Have these two liquids mixed on a
molecular level within a specified fraction (say 5%) of the mixing fraction which will be
attained in the whole vessel at infinite time?”, and it encodes the answer in the colors of the
evolving mixture. It is hoped that the simplicity of use and the directness of the mixing
information reported will stimulate experiments that provide substantial “engineering
insight” into the dynamics of mixing.
DISMT makes use of two standard acid-base indicators, methyl red (red to yellow,
pK ~ 5) and thymol blue (yellow to blue, pK ~ 9). Both indicators are added to both
unmixed solutions. A red (acidic) solution is mixed with a blue (basic) solution, and in
those regions where the mixing fraction is within 5% of the mixing fraction at infinite
time, the solution is yellow. With a clear mixing vessel, an observer may see distinct red
and blue regions as well as the later emergence of yellow regions. With DISMT, the 95%
mixing time for the entire vessel may be defined as the time for the entire liquid volume to
become yellow.
2
The following discussion of the role and utility of various mixing diagnostics
makes substantial use of a review developed as part of a student thesis[1]. The examples are
intended to be illustrative rather than exhaustive.
DISMT is a reaction-based diagnostic, and thus color changes occur only when
reactants have been mixed at the molecular level. Such reaction-based diagnostics avoid
the ambiguities associated with dilution diagnostics and the phenomena generally referred
to as “micromixing”[2]. With dilution based diagnostics, in which for example, a nonreactive tracer dye is added to a mixing tank, the finite sampling volume of any detection
system may include elements of liquid which are much smaller than the detection volume
but which have not mixed on a molecular level. The detector will report only the overall
mixing fraction and will not distinguish between dispersed and molecularly mixed fluids.
Many elegant reaction-based methods have been developed to characterize the rates
of mixing. These include the use of competitive parallel reactions [3-6], and fluorescencebased measurements of turbulent fluctuations[7-8]. The methods work well, but because
they make use of point-wise sampling, they report results which provide little insight into
the dynamics of the mixing process.
Colorimetric methods include inert and reactive dye tracers[9] and discoloration of
colored species by reactions[10]. When these methods are used in a volumetric – rather than
point-wise fashion, they can provide substantial information about the dynamics of mixing.
However, because the mixing information is encoded in the intensity of the transmitted
light, these methods can give ambiguous results along the line of sight. The “one
indicator” methods cannot give information about a range, say +/- 5% of ideal, for the
mixing fractions.
Planar laser induced fluorescence methods provide excellent spatial resolution,
without the ambiguities associated with viewing along the line of sight, for a selected plane
within the mixing vessel. A variety of mixing studies have made use of planar laser
induced fluorescence, with either simple dilution[11-14] or with acid-base reactions [15-22].
Most of the acid-base fluorescence studies have used fluorescein, whose fluorescence turns
on for pH>4. More recently, dual emission fluorescence systems have be described in
which mixing information is encoded in changes in the emission spectra rather than in
intensities[23]. A fluorescent diagnostic system in which the shift in the fluorescence of a
solvatochromatic dye was used to image the mixing fraction in a decane/ethanol system
has been described[1]. These last two systems, with their emphasis on spectra rather than
intensities, are analogous to the colorimetric DISMT system described in this work.
This paper describes: (1) the principles underlying and choices involved in the
design of DISMT systems, (2) protocols for carrying out DISMT-based experiments, and
(3) examples of results obtained with DISMT. Because the DISMT methods are cheap and
do not give fully quantitative information, it is expected that they will find their most
natural use in visualization for “engineering design”, i.e., in the heuristic design and testing
of mixing systems.
3
II.
Design of DISMT Systems
The fundamental idea underlying the DISMT method is that two color changes are
used to mark two acid-base mixing fractions, fl = (1-δ)*f∞ and fh = (1+δ)*f∞, where f∞ is
the acid mixing fraction at infinite time. By appropriate adjustment of the initial pH’s of
the two liquids to be mixed, the pH’s at these two mixing fractions will be the pKa of the
basic indicator and the pKa of the acidic indicator, respectively. However, a variety of
issues such as properties of appropriate pH indicators, routine use, sensitivity to mixing
fraction, and interpretation of the color changes must be addressed.
A. Acid-Base Chemistry
The chemistry underlying DISMT is that of a strong acid/strong base aqueous
titration in the presence of two weak acids, the pH indicators. The titration equation[24] is
(Ricci, 1952):
(1)
H – OH = as – bs + (aα)1 +(aα)2
where H = molar concentration of H+;
OH = molar concentration of OH-;
as = molar concentration of strong acid;
bs = molar concentration of strong base;
ai = molar concentration of indicator i (in both acid and base forms, i=1,2);
αi = fraction of indicator i in base form = Ai/(Ai +H), (i = 1,2);
Ai = acid dissociation constant for indicator i, = 10-pKai, (i=1,2).
In acid solution OH results from the water equilibrium (and vice versa for basic solutions),
and hence Equation 1 becomes, in fuller form,
H – W/H = H – W/OH = as –bs +a1A1/(A1+H) + a2A2/(A2+H)
(2)
where W is the dissociation constant for water. In any element of the mixing liquids, as =
f*aso and bs = (1-f)*bso, where aso is the concentration of strong acid in the initial, unmixed,
acid solution, bso is the concentration of strong base in the initial, unmixed, basic solution,
and f is the volumetric mixing fraction of the acid solution [= Va/(Va +Vb)]. Va and Vb are
the volumes of the acid solution and basic solution, respectively, in the element. The final
equation is as given in Equation 3:
H – W/H = f*aso – (1- f)*bso +a1A1/(A1+H) + a2A2/(A2+H)
(3)
If a1 = a2 = 0, Equation 3 describes a strong acid/strong base titration, in which the
pH changes strongly in the vicinity of log√W ≅ 7.00. Figure 1 shows the pH as a function
of the mixing fraction f, as calculated on the basis of Equation 3, for three such titrations:
a1 = a2 = 1 x 10-8 M, a1= 5 x 10-6 M, a2 = 2.5 x 10-6 M (DISMT system used in
demonstrations), and a1 = a2 =1 x 10-4 M. The first two curves are virtually identical. The
third curve differs substantially, an effect that will be discussed in Section IV.C.
Figure 1
4
If expanded, Equation 3 yields a quartic polynomial, and direct solution is not
feasible. It must be solved by iterative methods.
B.
Choice and Use of Indicators
The properties of an acid–base indicator which are most important are the colors or
the acid and base forms, the pKa at which the color changes, and the sensitivity to
environmental (temperature and ionic strength) effects. The indicator should also be
commercially available, be inexpensive, and have low toxicity.
1.
Desired pKa
In designing acid-base titrations for quantitative analysis, it is generally
recommended that a pH change of 1-2 units is necessary to cause a color change sufficient
to define a sharp end point. In the design of DISMT, the sharpest change of pH with
mixing fraction f occurs near pH = 7, and consequently acid-base indicators with pKa’s
close to 7 will show the sharpest color change with as a function of f. However, if the
pKa’s are too close to 7, small errors due to impurities can have significant effects. The
current DISMT system makes use of methyl red (pKa = 5.0) and thymol blue (pKa = 9.2) as
a compromise between sensitivity to mixing fraction and insensitivity to impurities.
2. Colors and Concentrations
As the pH increases, methyl red turns from red [ε(λmax = 522 nm) = 1.74 x
10 L/(M-cm)] to yellow [ε(λmax = 428 nm) = 1.58 x 104 L/(M-cm)] at about pH =5, and
thymol blue turns from yellow [ε(λmax = 432 nm) = 1.27 x 104 L/(M-cm)] to blue [ε(λmax =
595 nm) = 2.84 x 104 L/(M-cm)] at about pH = 9. Both indicators are yellow in the pH
range 5-9, the “mixed within tolerance” range, and thus the identification of yellow as
“mixed within tolerance” does not depend on the concentrations of the indicators. When
the pH is equal to the pKa for methyl red (concentrations of the acid and base forms of the
indicator are equal), the solution appears orange. When the pH is equal to the pKa for
thymol blue the solution appears green.
4
The DISMT method is designed so that pH(fl) = pKa(methyl red) and pH(fh) =
pKa(thymol blue), where fl = (1-δ)*f∞ and fh = (1 + δ)*f∞. Figure 2 illustrates this effect;
ideally, for f < fl the solution is blue, for fl < f < fh the solution is yellow, and for f >fh trhe
solution is red. Based on the experience gained in developing and testing the DISMT
method, it seems that most observers perceive the color change as sharpest for δ about a
factor of 2-3 larger than the design value of δ. Thus if one wishes an observer to perceive
the zones in which the liquids are mixed within 5% of f∞, the DISMT calculations should
be based on a δ which is a factor of 2-3 smaller than 0.05. In deciding what value of δ to
use, the user must judge what qualitative/semi-quantitative information is desired. [It is
quite possible that videotaping of the mixing experiment and subsequent computer-based
hue sensitive analysis of the images can resolve this question of perception, but such
techniques have not been pursued in this work. DISMT, as with any colorimetric method,
5
suffers from ambiguities along the line of sight, and the color of any particular portion of
the mixture, viewed through liquid of a different color, may be distorted.]
Figure 2
The apparent color changes are sharper for higher concentrations (greater optical
depth) of the indicators. Higher concentrations also result in sharper changes of pH with f,
even though the indicators also act as buffers (see Section IV.C.). The concentrations
described in this paper, 5 x 10-6 M and 2.5 x 10-6 M for methyl red and thymol blue,
respectively, seem appropriate for a mixing tank 1 foot in diameter. Lower concentrations
would be appropriate for larger tanks, and vice versa.
For the jet mixing experiments which were part of the development of the DISMT
method, the basic (blue) liquid was injected into initially quiescent acid (red) liquid. This
order was used because the blue liquid was perceived as more visible within the red liquid,
rather than vice versa.
3. Sensitivity to Environmental Effects
For methyl red, pKa = 5.00 – 0.006*(t-20), for µ < 0.5, where t is the
temperature in degrees centigrade and µ is the ionic strength. For thymol blue, the pKa is
independent of temperature for t = 15-30 C, but depends significantly on the ionic strength
(9.20, 9.01, 8.95, and 8.90, for µ = 0, 0.01, 0.05, and 0.10, respectively)[25] (Bishop, 1972).
In addition the pKa for water is temperature dependent[26] (Lide, 1982).
4. Other
Both methyl red and thymol blue are commercially available from a variety of
sources. Users should consult the MSDS documents prior to use.
III.
Experimental
A.
Reagents and Chemical Apparatus
Methyl red, thymol blue and phenolphthalein were purchased from Aldrich.
Approximately 0.100 N HCl and KOH were used to adjust the pH. De-ionized water was
used in all procedures. The pH meter and electrode (Orion 230A/9107 ATC triode) were
calibrated at 25 C with standard buffer solutions (pH = 7.00 and 10.00) purchased from
Fisher. Ethanol was purchased from Fisher. All reagents were used as received.
Stock solutions of the indicators were prepared as follows: 202 mg of methyl red
was dissolved in 200 mL ethanol (denatured)and filtered to remove undissolved particles.
10 mL of this solution in 7.5 L de-ionized water provided a concentration of 5E-6 M. 183
mg of thymol blue was dissolved in 200 mL ethanol (denatured) and filtered to remove
(numerous) particles. 10 mL of this solution in 7.5 L de-ionized water provided a
concentration of 2.5 x 10-6 M. The thymol blue solution appears to change color slightly
6
over the course of a few days, and it is recommended that it be prepared close to the time
of use.
B.
Mixing Experiments and Apparatus
A simple jet mixing tank (30 cm inside diameter, 136 cm high, 1 cm ports 2.5 cm.
from the bottom, 4 ports at 90 degrees) was used for developmental tests with the DISMT
system. The pumping/mixing system consisted of two channels, each with a 2.2 gal
reservoir, pump, recycle loop and valve, and flow meter and valve. Flow rates up to 8
L/min could be achieved. The mixed fluid in the tank could be drained back into the
reservoirs for reuse. In a typical test, 6 L of the acidic (red) solution was pumped into the
mixing tank, and then 6L of the basic (blue) solution was pumped into the mixing tank.
The entire procedure was videotaped in color from the side. Each video sequence included
a few seconds taping of a Color Checker® , a test pattern of 24 standard colors, to allow
subsequent standardization of video images[27] (Edmond, 1999). Figure 3 shows a
schematic diagram of the mixing apparatus.
Figure 3
C.
Preparation of Solutions to be Mixed
A program was prepared to accept input for a particular experiment (volumes to be
mixed, δ, desired concentrations of indicators, temperature, ionic strengths, etc.), solve
Equation 3 under various inputs, and provide output to the user. The program calculates
the amounts of indicator solutions to be added, the initial pH’s, the amounts of strong
acid/base to be added, and the composition of the test solutions. It also estimates the
precision with which a color change is associated with a particular δ.
The initial strategy was to use this program to calculate the desired initial pH’s,
carefully, calibrate the pH meter and electrode, and to add acid (or base) dropwise to adjust
the pH within ± 0.02 pH units. However, it was found that many effects must be
accounted for in order to measure the pH to this accuracy and precision. (calibration curve,
ionic strengths, sodium ion effects, temperature, etc), and reliable operation of the DISMT
method could not be achieved. The effective strategy was to use a program to calculate the
initial pH’s and the amounts of strong acid/base needed to achieve them. A colorimetric
procedure, described in the following paragraph, was then used iteratively to set the pH of
the base solution relative to that of the acid solution. Once this simple colorimetric setup
test was satisfied, satisfactory performance with the full scale mixing experiment was
reliably achieved.
In order to set up an experimental run, the calculated amounts of both indicators
were added to both reservoirs. By dropwise addition of dilute HCl/KOH the pH in both
reservoirs was adjusted to 7.0±0.5. The calculated amounts of 0.100 N HCl (KOH) were
added to the acid (base) reservoirs, respectively. Three 5.0 mL aliquots were pipetted into
12 mL vials, and three calculated volumes (Vred, Vyellow, and Vgreen), corresponding to
mixing fractions of f= (1-5*δ)*f∞, f∞, and (1+5*δ)*f∞, were added to the vials,
respectively. If the relative pH’s were correct, the three vials showed balanced
7
red/yellow/green colors (almost like a traffic light). If the base solution was not
sufficiently basic, the yellow appeared orange or orange/red. If the base solution was too
basic, the yellow appeared green or blue/green. Balance of the optical depth of the red,
yellow, and green solutions seemed to provide the most sensitive test. The best sensitivity
was achieved when the solutions were viewed down the axis of the vial rather than across
the vial, i.e., at the maximum optical depth. Figure 4 shows a sequence of such tests
including a well-balanced red/yellow/green sequence, which has been described as a
“traffic light”. It is best to conduct the mixing run within 30 minutes of adjustment of the
concentrations.
Figure 4
IV.
Results and Discussion
A.
Demonstration Mixing Experiment Using DISMT
Figure 5 shows a sequence of images obtained for a test mixing run with the DISMT
system. The system was prepared as described in the previous sections, including
balancing of the relative concentrations of the acid and base solutions with the “traffic
light” technique. 6.0 L of the acid solution (red) was pumped into the tank and allowed to
sit for approximately one minute. Then 6.0 L of the base solution (blue) was pumped into
the tank, and the valve was closed. The valve on the base jet side was opened to full as
quickly as possible, and once a little less than 6 L had been pumped, it was closed off as
quickly as possible. In the first 60 seconds, there is very little change in the color, although
with careful examination it is possible see portions of the blue jet which have not yet
completely reacted with the bulk red solution. In image (f), at 73 seconds, a base-rich zone
at the lower left corner appears. In image (g), at 83 seconds, the base-rich zone has grown,
and a zone of liquid with an orange and yellow color (mixing fraction near f∞) appears
across the top of the liquid. In image (h), at 93 seconds, the mixing fraction for the liquid
in the upper right corner of the tank is in the “mixed within tolerance” zone, the liquid in
the center of the tank is still acid, and the base-rich zone remains at the lower left corner
remains. In images (I), (j) and (k), the there is no more flow from the jet, and the liquid in
the tank slowly evolves toward a homogeneous mixture with final mixing fraction f∞, with
substantial zones of green and orange color (which are actually reasonably well mixed, i.e.,
0.05 < δ < 0.14, see Section IV.C.) Image (l) was taken after the tank had been manually
stirred. It shows the yellow color which is characteristic of the “mixed within tolerance”
DISMT design. [Note: In these and other sequences of images, the relative times are
accurate, but there may be an error of as much as 5 seconds in the absolute time.]
Figure 5
B. Comparison of DISMT with One Indicator Acid Base Methods
The range of interpretable colors shown in the Figure 5 DISMT color sequence can
provide substantial semi-quantitative information.. However, DISMT is somewhat more
complex to carry out than standard one-indicator methods, and it is worthwhile to compare
DISMT mixing results with those obtained with one-indicator methods.
8
Three comparisons were carried out. The volumes were the same as in the DISMT
demonstration. In the first two, the standard DISMT procedure was used, except that no
methyl red was added to the reservoirs. The concentration of the base solution relative to
that of the acid solution was adjusted using the “traffic light” balancing (without the red).
In the third, phenolphthalein (red in base, colorless in acid) was used as the only indicator
(6 x 10-6 M in each reservoir), and the concentration of the base solution relative to that of
the acid solution was adjusted as in the “traffic light” balancing. The middle vial was
clear. Figure 6 shows selected images from the one indicator mixing experiments. In the
left column, the acid (yellow) solution is injected from the left into the base (blue) solution.
The zones which have pH > pKa(TB) = 9.2 (fl = 0.475) appear blue; those with pH < 9.2
appear yellow. Very little information is provided about intermediate zones. The final
solution is yellow as a consequence of the colorimetric balancing procedure used to set up
the demonstration. In the center column the base solution is injected from the right into the
acid solution. The same general pattern of blue (pH > 9.2) and yellow (pH < 9.2) is seen,
and the final solution is yellow. In the right column, the acid (clear) solution is injected
from the left into the base (magenta) solution. The clear liquid is difficult to identify
through the magenta liquid, and the non-quantitative perception of color intensity by the
human eye makes it difficult to identify regions of good mixing. Since the intensity of the
magenta color increases continuously in the pH region 8- 9.8 [pK1/2(phenolphthalein) =
9.5.26], it is difficult to specify what the mixing fraction is at the transition from “weak
magenta” to “clear”. The increase in information available with DISMT, relative to the
one indicator methods, is substantial.
Figure 6
C. Interpretation of Color Change and Estimation of δ
Figure 2 seems to indicate that the color of the solution changes precisely at the mixing
fractions fl and fh. If this were so, then an observer could rigorously identify the yellow
zone as “mixed within tolerance”. In reality, the changes take place over a range of pH (a
phenomenon well known to students in quantitative analysis). In an attempt to estimate the
uncertainty in identification of the “mixed within tolerance” zone, calculations of the error
in estimation of fl and fh (and consequently, δ) were carried out.
At pH = pKa(MR), the solution appears orange, and at pH = pKa(TB), the solution
appears green. Many observers, however, will focus on the red and blue of the initial
solutions and will identify the “mixed within tolerance” zone as “yellow only” rather than
“orange through green (inclusive)”. The perceived δ for these observers is smaller than the
design δ. Other observers will identify the “mixed within tolerance” zone as “neither red
nor blue”, and their perceived δ will be larger than the design δ. Using Equation 3, mixing
fractions were calculated for pH = pKa(MR) ± ∆pH and pKa(TB) ± ∆pH. For ∆pH = 0.5,
the ratio of the acid to the base form of the indicator changes by about a factor of three
from that at pH = pKa. Other values of ∆pH could be used, but this one seems realistic.
Figure 7 shows the results of such calculations for the actual DISMT system used in the
demonstration mixing experiments, for which δ = 0.05, f∞ = 0.50, fl = 0.475, and fh =
0.525. The leftmost, rightmost, and center zones would almost always be perceived as
blue, red, yellow, respectively. An observer with a “yellow only” criterion would impose
9
the requirement that 5.5 < pH < 8.7, which corresponds to 0.492 < f < 0.509, or δ ≅ 0.016.
An observer with a “neither red nor blue” criterion would impose the requirement that 4.5
< pH < 9.7, which corresponds to 0.423 < f < 0.570, or δ ≅ 0.14. The ambiguities
described here would appear also in the determination of a mixing time.
Figure 7
The analysis described in the previous paragraph, taken in conjunction with the
calculations shown in Figure 2, implies that use of higher concentrations of the acid-base
indicators leads to more precise limits on the estimated value of δ. The indicators act as
buffers and make the pH changes as a function of mixing fraction slower. However, the
imposition of the requirements that pH(fl) = pKa(TB) and pH(fh) = pKa(MR) results in the
use of stronger acid and base solutions. The net result is a higher value of the slope for f ≤
fl and for f ≥ fh (see Figure 2), and closer error limits on δ for an observer using the
“neither red nor blue” criterion. The limits on δ for the “yellow only” criterion are
virtually unchanged. A calculation analogous to that shown in Figure 7, but for a1 = a2 = 1
x 10-4 M, results in δ = 0.11 for the “neither red nor blue” criterion.
B.
Determination of Mixing Time Using DISMT
For many mixing experiments, the mixing time is defined as “the time for all of the
liquid to become mixed within 5% (or 1%, or 0.1%) of the infinite time mixing fraction”.
The DISMT system described in this paper enables an observer to examine the entire
volume of the mixing region and, through observation of the colors within the system, to
determine when all portions of the liquid are yellow, i.e., “mixed within tolerance”. The
observer does not need to make prior judgements about where to place colorimetric probes
(which may perturb the flows) or where to place the PLIF laser sheet. The concentration
information which DISMT provides is semi-quantitative but incisive: the yellow color is
the region in which the liquids are “mixed within tolerance”. The mixing time is
unambiguously the time to achieve a uniform yellow color.
The colorimetric DISMT system is designed for “engineering insight” experiments. It
is cheap and simple, with low toxicity reagents, and the mixed liquids can be drained back
into the reservoirs, the acid and base concentrations easily readjusted, and the same
reagents reused.
DISMT is direct, readily used, and specific for determination of the mixing time for
molecular level mixing. It should be evaluated as a potential standard method for use by
research scientists/engineers and by both purchasers and vendors of mixing equipment.
C.
Future Work
In some cases, spatially precise information about the effectiveness of mixing is
required, as for example, in the region near the tip of an impeller blade. For this situation
and other such needs, a PLIF version of DISMT is under development: a characteristic
color of fluorescence will identify the regions in which the liquids are “mixed within
tolerance”. In addition many mixing problems involve liquids with viscosities
10
substantially higher than the viscosity of water. There appears to be no fundamental
limitation in the DISMT chemistry which would conflict with the addition of appropriate
polymeric viscosity enhancers, and thus it is anticipated that DISMT will be adapted for
such uses also.
V.
Acknowledgements
The authors wish to acknowledge the support and encouragement of Ann Butlzer
and R. Page Shirtum of The Dow Chemical Company. LAM wishes to acknowledge the
award of a Special Faculty Development Assignment by the University of Texas at Dallas
and additional support by The Dow Chemical Company, which made possible the
development of this diagnostic method and a year of valuable learning about the chemical
process industry.
VI.
Disclaimer
The material presented in this paper is believed to be accurate. However no
warranty is given or implied, and The Dow Chemical Company assumes no responsibility
for its use by others.
VII
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13
Figure Captions
1.
pH versus mixing fraction f
2.
pH versus mixing fraction. Vertical lines are the values of fl and fh (pH = pKa). In
a ideal DISMT system, for f < fl, the solution is blue; for fl < f < fh, yellow; and for
f > fh, red.
3.
Schematic view of mixing apparatus (side view, only one
reservoir/pump/flowmeter system is shown)
4.
Colors obtained in colorimetric pH balance procedure (traffic light). (a) base
concentration is significantly weak compared to the acid solution, column, (b) base
concentration is modestly weak, (c), correct balance, (d), base concentration is
modestly strong, and (e) base concentration is significantly strong.
5.
Jet mixing sequence obtained with DISMT method. Time is in seconds after the
start of the mixing flow (jet is from the right)
6.
Jet mixing sequences obtained with one indicator methods. Time is in seconds
after the start of the mixing flow. For the mixing of acid (yellow) solution into
base (blue) [left column] and for the phenolphthalein mixing[right column], the jet
is from the left; for the mixing of base (blue) into acid (yellow) [center column] the
jet is from the right.
7.
Estimation of δ for ∆pH = 0.5. a1 = 5.0 x 10-6 M; a2 = 2.5 x 10-6 M. Vertical lines
are the values of the mixing fraction which correspond to pH = pKa ±∆pH.
14
12
11
10
9
8
actual
concentrations
a1=a2=1 x 10(-8) M
pH 7
a1=a2=1 x 10(-4) M
6
5
4
3
2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
mixing fraction
DISMT-Melton-FIGURE 1
15
12
11
10
9
8
actual concentrations
a1=a2=1 x 10(-4) M
pH 7
f = 0.475
f = 0.525
6
5
4
3
2
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
mixing fraction
DISMT-Melton-FIGURE 2
16
MIXING
TANK
FLOWMETER
TO
DRAIN
RESERVOIR
PUMP
DISMT-Melton-Figure 3
17
DISMT-Melton-FIGURE 4
18
DISMT-Melton-FIGURE 5
19
DISMT-Melton-FIGURE 6
20
12
11
10
9
8
pH
7
6
5
4
3
2
0.40
0.45
0.50
0.55
0.60
mixing fraction
DISMT-Melton-FIGURE 7
21